She was doubtless just as nervous as any other student on work experience, but the sober-suited blonde spotted walking through Lincoln's Inn Fields, headquarters of the British legal establishment, just before Christmas was not just any old intern.

And the role taken by Chelsy Davy, Prince Harry's girlfriend, at Farrer & Co - solicitors to the Queen - was not just any old placement. The next day's newspapers pondered uncharitably how many Leeds University students would have got the same break.

Davy might well, of course, have owed her luck purely to her legal skills, but the cosy networks helping many children of the professional middle classes into successful careers - the summer job in the City, the internship that is never openly advertised, the unpaid gofer job in the theatre eased by parental subsidy - are now coming under scrutiny.

A review of barriers to working-class entry to the professions, led by former cabinet minister Alan Milburn, will investigate not just visible causes of social inequality - children from the highest socio-economic group are nearly three times more likely than those from the lowest to get good GCSEs, and six times more likely to go to university - but more insidious factors. Its conclusions will feed into a white paper on social mobility being launched this week by Cabinet Office minister Liam Byrne.

Its timing during a recession is provocative, but senior Labour figures have long wrestled with this dilemma. Last summer the then arts minister Margaret Hodge began privately arguing for government assistance for poorer children breaking into the arts, amid fears that creative careers were too often reserved for those whose families could support them while they worked unpaid.

Discrimination at the bar was raised nearly a decade ago by Euan Blair's mother, Cherie Booth, a self-confessed "working-class scouser" turned QC who denounced the funding of pupillages as a "scandal" discriminating against poorer applicants. Milburn, brought up on a council estate by his single mother, has long been interested in the issue.

Nonetheless, invoking the emotive issue of class just as rising unemployment inflames resentment of the rich will arouse suspicion. Downing Street has been poring over focus group findings suggesting that their "do nothing" charge against the Tories was reviving forgotten perceptions of the Conservatives as unsympathetic to the poor during the last recession - undermining Cameron's portrayal of his party as modern and compassionate.

Aides believe that last week's promise to cut taxes for savers worried about low returns on their nest eggs opens Cameron to charges of defending a wealthy elite. "We didn't even set them a trap," says one Downing Street aide, "but they've walked into it."

Yet class politics has pitfalls too, as Gordon Brown found when he entered the row over Laura Spence, a state school pupil refused a place to study medicine at Oxford University despite excellent predicted grades, triggering a national debate over whether top jobs were still shrouded in old-fashioned snobbery.

That row blurred some awkward facts: some of the candidates who beat Spence had state school backgrounds, while she herself later said: "I don't feel being from a comprehensive mattered in my case." Eight years on, only 10% of Oxbridge students come from working-class families. Can yet another review really break down such entrenched social divides?

Sitting on the shelf behind Liam Byrne in his constituency office, in the rundown Birmingham suburb of Hodge Hill, is a brightly wrapped box labelled "Time Capsule 2020". It contains a bundle of carefully coloured-in sheets of paper detailing the future dreams of a group of local 11-year-olds.

There are a few who want to be footballers and beauticians when they grow up, but most aspire to solidly middle-class professions. They want to be doctors, teachers and lawyers. But their tragedy is that, unless something fundamental changes, too few will make it: Hodge Hill is in the bottom 5% of the country for sending children to university, and has the fourth highest unemployment rate. So what happens between 11 and 18 to crush such dreams of a life very different from their parents'?

Byrne should know: his first job on leaving his Essex comprehensive was in McDonald's, yet he went on to university and an international career in management consultancy before entering politics. Why did he succeed where others failed? "I had parents who loved me and pushed me and picked me up when I got things wrong."

The paper that Byrne is launching this week will argue that there is no one solution to unlocking social mobility: rather, a constant process of levelling the playing field at all stages in life. "The evidence says that there isn't a silver bullet, there's no one thing you can do to boost social mobility: you have got to act at every stage in someone's life," he says.

Byrne argues that political differences over coping with recession have opened an argument about privilege and how it passes between generations. "I'm not advocating class war: I am arguing for a battle for the majority on behalf of the majority. Cameron has revealed that not only is he not a man for the majority, he's not a man for the middle classes either. When you look at his [savings] tax policies they don't touch 60% of pensioners."

He argues that Cameron may be good at cultivating an everyman image "about what tea he drinks and what kind of a kettle he would buy" but his party is reverting to type in arguing against greater investment in public services. Ministers will argue this week that such spending will create jobs and so increase "room at the top" in professional and managerial careers for poorer children when the upturn comes.

The Tories, who published their own social mobility paper recently, will fight back by focusing on school reforms including a proposed "pupil premium" in spending on poor students, encouraging schools to nurture them. The shadow education secretary, Michael Gove, the adopted son of a fish merchant, has noted that, of the 13,500 children who got three As at A-level last year, only 189 were on free school meals.

Both sides agree the golden age of social mobility was the 1950s, when the birth of the welfare state and growth in professional jobs swelled the middle classes: almost 40% of those born to fathers in the lowest income group in 1958 advanced into the top two income groups. By 1970, only 33% were moving up: rates have remained broadly static since.

But amid new global competition for jobs, can the logjam at the top of British society be unblocked without a painful readjustment for the middle classes?

Brown will argue this week that a billion new skilled jobs will be created worldwide over the next decade, presenting opportunities for a 1950s-style explosion of professional positions. The strategy unit report also suggests that upskilling could turn previously menial jobs into real careers: childcare could evolve into a teaching-style profession.

But first Britain must survive a recession forecast to hit the middle classes hard. Competition for places in the best state schools, the first rung on the ladder, will intensify as parents withdraw from unaffordable private education: with rising numbers of children getting degrees, formal qualifications may start to matter less than the informal networks used so well by the middle classes.

Gove argues that the recession may help break up cosy old-boy networks: "If you have people who have acquired jobs on the basis of connections but whose ability isn't strong then they are the first that are likely to be shed." However, he adds, middle-class children are also more likely to have gained the hard qualifications employers will now be looking for.

Byrne admits that it is impossible to stop middle-class parents playing the system, but insists it is a "classic liberal error" to assume they have to suffer in order to give others a fair chance.

"We have got to create more room at the top again, by bringing to Britain the jobs that will be created around the world," he says.

Nonetheless this week's proposals are likely to bring calls from the Labour left for more radical assaults on privilege. The children of Hodge Hill may still have a mountain to climb.

Privately educated

Cabinet ministers who were educated in private schools:

Alistair Darling: Loretto School, Musselburgh

Ed Balls: Nottingham High School

Jack Straw: Brentwood School, Essex

Geoff Hoon: Nottingham High School

Harriet Harman: St Paul's Girls', London

James Purnell: Royal Grammar School, Guildford

Shaun Woodward: Bristol Grammar

• This article was amended on Thursday 22 January 2009. Laura Spence was refused a place to study medicine at Oxford, not Cambridge, University. This has been corrected.